Sure! Let's go through the given problem step-by-step.
First, we have two defined events:
- Event [tex]\( A \)[/tex]: The student plays basketball.
- Event [tex]\( B \)[/tex]: The student plays soccer.
We are given some probabilities:
- [tex]\( P(A \text{ and } B) \)[/tex]: The probability that the student plays both basketball and soccer, which is [tex]\( \frac{2}{10} \)[/tex].
- [tex]\( P(B) \)[/tex]: The probability that the student plays soccer, which is [tex]\( \frac{2}{5} \)[/tex].
We need to find [tex]\( P(A \mid B) \)[/tex], which is the conditional probability that the student plays basketball given that they play soccer. The formula for conditional probability is:
[tex]\[
P(A \mid B) = \frac{P(A \text{ and } B)}{P(B)}
\][/tex]
Given:
[tex]\[
P(A \text{ and } B) = \frac{2}{10} = 0.2
\][/tex]
[tex]\[
P(B) = \frac{2}{5} = 0.4
\][/tex]
Now we can plug these values into the formula for conditional probability:
[tex]\[
P(A \mid B) = \frac{P(A \text{ and } B)}{P(B)} = \frac{0.2}{0.4}
\][/tex]
Simplifying this:
[tex]\[
P(A \mid B) = 0.5
\][/tex]
Thus, the correct answer is:
C. [tex]\(\frac{2}{4} = 0.50\)[/tex]
